AP Lux is the best champion. Forget Janna (but keep her in your heart), forget Lulu (but save a special spot in your memories), and don't even think about Kayle (except on holidays). Lux is like Morgana in her nasty utilities and damage output, except she never gets banned in draft pick! Also, her gigantic laser ult is hysterically unfair. Firing the main cannon!

Suggestions? I see a lot of people building HoG and philosopher's but usually just skip them to build warmog's

If you want to give your blue away you're gonna have to get that Philo Stone, otherwise you'll be pretty low on mana. If you don't have enough for at least an E+Q combo at (Relatively) all times then something's wrong. Sometimes I just spam my skills for shits with him and it costs me my life for exactly the reason that I don't have said escape/initiation ready.

Also, both Philo and HoG means you can spend more time ganking and less time farming and still get a good chunk of gold thanks to it. Jarvan's strong suit is, indeed, ganking. His clear times are meh.

oh my god why do junglers always stand in the fucking bush and wait there for 5 seconds, every time they do it to me they just fucking stand there and watch the enemy run back a few steps, and when they finally decide to quit fapping and run in, the enemy gets away with 20 hp

I find supports hard to play though. And speaking of Lux, is she mana hungry? Ｔｈｉｎｋｉｎｇ ｏｆ ｇｅｔｔｉｎｇ ｈｅｒ．

Lux can chew threw mana pretty quick if you're going balls out with her, but she's definitely one of the stronger support champs, and her CC can shut people down quite well. Plus, if you chain her combo right, she can burst people down as well as most AP carries.

But any and all flaws are totally voided by her ridiculous ult. It's definitely my favorite closer in the game. Every twenty-five seconds, you can unleash a massive laser blast that deals huge damage at extreme ranges. So damn fun, and extremely satisfying to launch at enemy champs who are fleeing from the action. They get halfway back to their spawn, thinking their totally home-free, and PAZOW!

Sometimes I like to go in the jungle near the entrance to the bad-guy base and just fry people running away from teamfights.

But, even if you don't like her, she's not terribly awfully expensive.

The fact I was laning against Teemo and Singed early game didn't help my cause eh?

Managed to get a kill on Singed but only because he tower-dived me when I had no HP, I ult'd and got a lot of HP back, so he died.

Renekton is very powerful, but he's easily counterable by sustain/harrass champions. If their solo is someone like Garen, wukong, or any melee champion, chances are you will tear them to bits.
And yeah your 1v2 didn't help.